Mathematics Question and Solution
tan60 = a/5
a = 5√(3) cm.
Where a is AD.
b = ½(a)
b = ½(5√(3)) cm
c = atan((½(5√(3))/5)
c = atan(½√(3))
Where c is angle AGB
d = atan(5√(3)/5)
d = atan(√(3))
Where d is angle CAG.
e = 180-c-d
e = 180-atan(½√(3))-atan(√(3))
e = 79.10660535087°
Where e is angle AFG.
Therefore;
(5/sin79.10660535087) = (f/sin(atan(√(3))))
f = 4.40958551844 cm.
Where f is FG.
It implies;
Shaded Area is;
Area triangle with height 4.40958551844 cm and base 5sin(atan(0.5√(3))) cm.
= 0.5*4.40958551844*5sin(atan(0.5√(3)))
= 7.21687836487 cm²
